ClimateMasterTranquility unit 2,5 years old In the last 6 months, WHEN FAN REACHES DESIRED TEMPERATURE WHEN FAN SHUTS OFF MAKES A LOW, LONG SIREN SOUND The authorized climate master repair service, cannot find the problem or cause of sound. CAN ANYONE HELP OR IS AWARE OF THIS SAME ISSUE MIAMI FL.

Nothing caught in the blower? Physically just hoping all is checked (that fan cage) in the blower housing Constant fan idling is common with GT systems and provides household evenness in comfort sometimes. -Seems all 'noise' then would depend on if it is reduced by just slowing to an idle-speed 24/7.
? How does 'FAN-"ON" position at the thermostat affect shut-off sound to 'idle speed' circulation operation, then?

Variable's frequencies of sounds , - vary -, in starts and shut-downs.

Some systems allow one to even pick off fan speeds to a 1/100th at a selected 'cfm' = air movement selected by cubic feet per minute./ Other systems have included, and better, as well as programing the compressor selected-staging running frequencies just to avoid 'noise' in rumbles to sirens sounds.

Is it when fan shuts down or when the Heat Pump/Compressor shuts down. Try it with just the fan on and off switch. My immediate suspicion when you describe siren like sound when temperature is reached has alarm bells going off in my head that it is a water valve. Water valves can make all sorts of noises if they don't close completely or as they're closing.